The Physics of a Perfect Three-Point Shot

It's more than just skill. It's science.

March Madness is over, and the University of North Carolina Tar Heels are officially the 2016-2017 college basketball champions. This year’s tournament was inundated by an insane amount of close games thanks to a marked spike in three-point shots. In a way, it makes sense: The NBA has created an industry of 3-point machines, with the Golden State Warriors and the Houston Rockets leading the league.

But what makes a perfect 3-point shot? Regardless if a player is in the NBA or NCAA, it all comes down to a little bit of luck and a triple threat of physics.

Angle

First thing first: Angle is everything. The angle of your shot will dictate how the basketball flies towards and into the hoop. The angle’s upward bound and forward distance is so important, in fact, that it dictates whether the ball has any chance of making it into the basket in the first place.

Gintaras Duda, a physics professor at Creighton University, did some calculations to figure out the lowest arc a player could shoot a basketball. The magic lower bound angle: 33 degrees.

Duda says, however, that the most optimal three-pointer has an arc of 45 degrees, with a speed of just under 20 miles hour at a spin rate of 2 revolutions per second. Duda’s calculations, it should be noted, account only for three-pointers at the collegiate level, where the line is set at 20 feet, 9 inches from the rim; the NBA’s furthest bound goes to 23 feet, 9 inches. Adjusting for a faster ball speed, however, leads to the same results, regardless of level.

The Magnus Effect

The Magnus effect — how the ball spins — is the second ingredient to the perfect three-point shot. A ball spinning in the air won’t move in a straightforward path — the force of moving air around the ball will cause a concerted change in velocity and create a curved path instead of a clean one.

In basketball, a player typically shoots a ball in a motion that puts a backspin on the ball. The Magnus effect means the backspin will lift the ball as it pushes forward, raising the arc, and creating a more favorable downward descent into the rim. The backspin also slows the ball down as it begins to descend, which could allow for a softer rebound should the ball hit the rim, or slow down the impact off the backboard and tip the ball to fall into the net. Either way, you’ve got three points.

Speed

There’s arc, there’s spin, and then there’s perhaps the most important of the holy trinity formula in making consistent three-pointers: speed. With virtually no margin of error when it comes to speed, it’s critical to harvest just the right amount of force. There’s a little bit of leeway in what kind of angle the shot has — a higher arc will have an easier chance of making a clean dip into the rim — but the speed has no variable and is a clear win or lose. Put enough force into the shot, or risk falling short, overshooting the rim, and even losing the game.